Hierarchical description of uncertain information

Humans have the innate ability to cope with and process incomplete and uncertain information. Any intelligent system should also have such an ability built in. Incomplete and uncertain information is formalized in different ways. By analyzing different methods for representing uncertain information, we propose a new method that uses a hierarchical coordinate to describe a total-order structure. This novel method describes information in different granular spaces by using hierarchical coordinates. The relationships among these spaces are constructed such that the transformation of information is possible. We extend the fuzzy equivalence and tolerance relations to weighted equivalence and tolerance relations, respectively. The properties of those relations and the isomorphism discriminant of information are described by using matrices. We develop a method for solving a complex problem with hierarchical coordinates. Simulation experiments demonstrate that a hierarchical coordinate system can help us to efficiently determine the optimal paths of large-scale networks.